We have an initial information wherein it’s given that the initial investment is $34 in the
year 1985 on a set of basketball card. Again, there’s a change in the book price by the
year 1995(10years later) and now it becomes $9800.We need to find out an equation for
the worth of the set at time t years, considering a constant percentage return in this
investment. We need to find out another thing, which is the value of the book in 2005, at
the same rate of return
According to the basic formulas: P(1 r )nt where
n
P principle, r rate of interest,
t time, n number of times compounded annually
Exponential rise(+)/Exponential depreciation(-)=
v(t) value at time, t , r rate of interest
Linear depreciation v(t) mt b
v(t) Ae(rise/ depreciation)*r*t where
Now, in the year 1985, the value was $34
10 years later, in the year 1995, the value becomes $9800
According to the basic formulas: P(1 r )nt where
n
P principle, r rate of interest,
t time, n number of times compounded annually
Here P principle 34, r rate of interest, t time 10, n 1 number of times
compounded annually
34(1 r)
10
9800
(1 r)
10
9800
34
1
1 r 9800
10
34
Thus,
1
r 9800
10
1
34
1
r (288.235294)10 1
r 0.762
Therefore, in the year 2005 that is, after 20 years, the value becomes
34(1.762)20 2824705.88 , we get this from the basic formula
Exponential rise(+)/Exponential depreciation(-)=
v(t) value at time, t , r rate of interest
v(t) Ae(rise/ depreciation)*r*t where
We have to consider exponential increase here, so v(t) Aer*t
v(t) value at time, t , r rate of interest
v
(0)
34
Ae
r*0
A
------(i)where
Initially
A
34
Thereby,
v(10) 9800 34e
10*r
9800 e10*r
34
, here
A
34,
t
10,
v
(10)
9800
Applying natural logs on both the sides, we get
r
1 ln(9800)
10 34
We need to find out an equation for the worth of the set at time t years, considering a
constant percentage return in this investment.
Thus , comparing with(i), we get,
1 ln( 9800 )t
v(t) 34e10 34
In the year 2005 that is, after 20 years, the value becomes $2824705.88.
The equation for the worth of the set at time t years, considering a constant percentage
1 ln( 9800 )t
return in this investment is v(t) 34e10 34